Structure and controller optimization for enhanced performance of magnetic levitation planar motors

Kai Liu , Fuxiang Chen , Xinpeng Wei , Aoqi Hu , Yingtong Wu , Xiaoqing Li , Lizhan Zeng

ENG. Mech. Eng. ›› 2026, Vol. 21 ›› Issue (4) : 100901

PDF (4835KB)
ENG. Mech. Eng. ›› 2026, Vol. 21 ›› Issue (4) :100901 DOI: 10.1007/s11465-026-0901-7
RESEARCH ARTICLE
Structure and controller optimization for enhanced performance of magnetic levitation planar motors
Author information +
History +
PDF (4835KB)

Abstract

The magnetic levitation planar motor utilizes electromagnetic force directly to achieve a six-degree-of-freedom motion. The magnitude and fluctuations of the electromagnetic force directly determine system’s acceleration and motion accuracy. This paper comprehensively improves the performance of magnetic levitation planar motor through structure optimization and controller design. A novel magnet array is adopted to enhance acceleration while establishing a precise analytical model for harmonic electromagnetic forces and analyzing the loop gain fluctuations. The optimized structure achieves an acceleration increase of over 58% while reducing higher-order harmonics by more than 34%. A fractional-order PIλDμ controller is employed to enhance design flexibility, utilizing gain margin, phase margin, and flat phase feature as constraints for a robust and high-bandwidth solution. Compared with the PID controller’s bandwidth of 16.74 Hz, the PIλDμ controller’s bandwidth is increased by 52%, reaching 25.57 Hz. Experiments validate the reliability of electromagnetic modeling and the controller design strategy.

Graphical abstract

Keywords

gain fluctuations / electromagnetic modeling / high-order harmonics / magnetic levitation planar motor / fractional-order PIλDμ controller

Cite this article

Download citation ▾
Kai Liu, Fuxiang Chen, Xinpeng Wei, Aoqi Hu, Yingtong Wu, Xiaoqing Li, Lizhan Zeng. Structure and controller optimization for enhanced performance of magnetic levitation planar motors. ENG. Mech. Eng., 2026, 21 (4) : 100901 DOI:10.1007/s11465-026-0901-7

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Steinbuch M , Oomen T , Vermeulen H . Motion control, mechatronics design, and Moore’s law. IEEJ Journal of Industry Applications, 2022, 11(2): 245–255

[2]

Compter I J C . Electro-dynamic planar motor. Precision Engineering, 2004, 28(2): 171–180

[3]

Kim W J , Trumper D L . High-precision magnetic levitation stage for photolithography. Precision Engineering, 1998, 22(2): 66–77

[4]

Oomen T . Advanced motion control for precision mechatronics: control, identification, and learning of complex systems. IEEJ Journal of Industry Applications, 2018, 7(2): 127–140

[5]

Dai L Y , Li X , Zhu Y , Zhang M , Hu C X . The generation mechanism of tracking error during acceleration or deceleration phase in ultraprecision motion systems. IEEE Transactions on Industrial Electronics, 2019, 66(9): 7109–7119

[6]

Jansen J W , Van Lierop C M M , Lomonova E A , Vandenput A J A . Modeling of magnetically levitated planar actuators with moving magnets. IEEE Transactions on Magnetics, 2007, 43(1): 15–25

[7]

Rovers J M M , Jansen J W , Lomonova E A , Ronde M J C . Calculation of the static forces among the permanent magnets in a Halbach array. IEEE Transactions on Magnetics, 2009, 45(10): 4372–4375

[8]

Min W , Zhang M , Zhu Y , Chen B D , Duan G H , Hu J C , Yin W S . Analysis and optimization of a new 2-D magnet array for planar motor. IEEE Transactions on Magnetics, 2010, 46(5): 1167–1171

[9]

Zhang L , Kou B Q , Xing F , Zhang H . Analysis and comparison of two two-dimensional Halbach permanent magnet arrays for magnetically levitated planar motor. Journal of Applied Physics, 2014, 115(17): 17E704

[10]

Peng J R , Zhou Y F . Modeling and analysis of a new 2-D Halbach array for magnetically levitated planar motor. IEEE Transactions on Magnetics, 2013, 49(1): 618–627

[11]

Peng J R , Zhou Y F , Liu G D . Calculation of a new real-time control model for the magnetically levitated ironless planar motor. IEEE Transactions on Magnetics, 2013, 49(4): 1416–1422

[12]

Wang Y , Chen F X , Zheng Z Y , Zeng L Z . Magnet array of planar motor using permanent magnets with different magnetisation intensity and height. IET Electric Power Applications, 2020, 14(14): 2772–2779

[13]

Zhang S G , Dang X P , Wang K , Huang J T , Yang J X , Zhang G H . An analytical approach to determine coil thickness for magnetically levitated planar motors. IEEE/ASME Transactions on Mechatronics, 2017, 22(1): 572–580

[14]

Guo L , Zhang H , Galea M , Li J , Gerada C . Multiobjective optimization of a magnetically levitated planar motor with multilayer windings. IEEE Transactions on Industrial Electronics, 2016, 63(6): 3522–3532

[15]

Min W , Zhang M , Zhu Y , Liu F , Duan G H , Hu J C , Yin W S . Analysis and design of novel overlapping ironless windings for planar motors. IEEE Transactions on Magnetics, 2011, 47(11): 4635–4642

[16]

Dai L Y , Li X , Zhu Y , Zhang M . Enhancing settling performance of precision motion systems by phase-based variable gain feedback control. IEEE Transactions on Industrial Electronics, 2021, 68(5): 4099–4108

[17]

Wang Z , Hu C X , Zhu Y , Zhu L M . Prediction-model-based contouring error iterative precompensation scheme for precision multiaxis motion systems. IEEE/ASME Transactions on Mechatronics, 2021, 26(5): 2274–2284

[18]

Meng Y X , Wang X Y , Huang W W , Li L L , Hu C X , Zhang X Q , Zhu L M . Intelligent tracking error prediction and feedforward compensation for nanopositioning stages with high-bandwidth control. IEEE Transactions on Industrial Informatics, 2023, 19(5): 6460–6470

[19]

Kenton B J , Leang K K . Design and control of a three-axis serial-kinematic high-bandwidth nanopositioner. IEEE/ASME Transactions on Mechatronics, 2012, 17(2): 356–369

[20]

Hu C X , Wang Z , Zhu Y , Zhang M , Liu H . Performance-oriented precision LARC tracking motion control of a magnetically levitated planar motor with comparative experiments. IEEE Transactions on Industrial Electronics, 2016, 63(9): 5763–5773

[21]

Huang S D , Peng K Y , Cao G Z , Wu C , Xu J Q , He J B . Robust precision position tracking of planar motors using min-max model predictive control. IEEE Transactions on Industrial Electronics, 2022, 69(12): 13265–13276

[22]

Dastjerdi A A , Astolfi A , HosseinNia S H . Frequency-domain stability methods for reset control systems. Automatica, 2023, 148: 110737

[23]

Han J L , Shan X L , Liu H T , Xiao J L , Huang T . Fuzzy gain scheduling PID control of a hybrid robot based on dynamic characteristics. Mechanism and Machine Theory, 2023, 184: 105283

[24]

Joseph S B , Dada E G , Abidemi A , Oyewola D O , Khammas B M . Metaheuristic algorithms for PID controller parameters tuning: review, approaches and open problems. Heliyon, 2022, 8(5): e09399

[25]

Podlubny I . Fractional-order systems and PIλDμ-controllers. IEEE Transactions on Automatic Control, 1999, 44(1): 208–214

[26]

Saidi B , Amairi M , Najar S , Aoun M . Bode shaping-based design methods of a fractional order PID controller for uncertain systems. Nonlinear Dynamics, 2015, 80(4): 1817–1838

[27]

Luo Y, Chen Y Q. Fractional Order Motion Controls. Chichester: John Wiley & Sons, 2012

[28]

Chen P C , Luo Y . An analytical synthesis of fractional order PIλDμ controller design. ISA Transactions, 2022, 131: 124–136

[29]

Chen P C , Luo Y , Peng Y B , Chen Y Q . Optimal robust fractional order PIλD controller synthesis for first order plus time delay systems. ISA Transactions, 2021, 114: 136–149

[30]

Abdulwahhab O W . Design of a complex fractional order PID controller for a first order plus time delay system. ISA Transactions, 2020, 99: 154–158

[31]

Chen P C , Zheng W J , Luo Y , Peng Y B , Chen Y Q . Robust three-parameter fractional-order proportional integral derivative controller synthesis for permanent magnet synchronous motor speed servo system. Asian Journal of Control, 2022, 24(6): 3418–3433

[32]

Chen P C , Luo Y . Analytical fractional-order PID controller design with Bode’s ideal cutoff filter for PMSM speed servo system. IEEE Transactions on Industrial Electronics, 2023, 70(2): 1783–1793

[33]

Arulvadivu J , Manoharan S , Lal Raja Singh R , Giriprasad S . Optimal design of proportional integral derivative acceleration controller for higher-order nonlinear time delay system using m-MBOA technique. International Journal of Numerical Modelling, 2022, 35(6): e3016

[34]

Kou B Q , Xing F , Zhang L , Zhang C N , Zhou Y H . A real-time computation model of the electromagnetic force and torque for a maglev planar motor with the concentric winding. Applied Sciences, 2017, 7(1): 98

[35]

Sun H B , Cheng R , Yang K M , Zhu Y , Lu S . Torque ripple error compensation of high-dynamic coil array commutation algorithm for magnetic levitation planar motor. IET Electric Power Applications, 2020, 14(5): 809–817

[36]

Zhu H Y , Teo T J , Pang C K . Magnetically levitated parallel actuated dual-stage (Maglev-PAD) system for six-axis precision positioning. IEEE/ASME Transactions on Mechatronics, 2019, 24(4): 1829–1838

[37]

Rovers J M M , Jansen J W , Lomonova E A . Multiphysical analysis of moving-magnet planar motor topologies. IEEE Transactions on Magnetics, 2013, 49(12): 5730–5741

[38]

Izci D , Ekinci S . A novel-enhanced metaheuristic algorithm for FOPID-controlled and Bode’s ideal transfer function–based buck converter system. Transactions of the Institute of Measurement and Control, 2023, 45(10): 1854–1872

[39]

Izci D , Ekinci S . Fractional order controller design via gazelle optimizer for efficient speed regulation of micromotors. e-Prime – Advances in Electrical Engineering, Electronics and Energy, 2023, 6: 100295

[40]

Can Ö, Ekinci S, Izci D. Honey badger algorithm for adjustment of FOPID controller adopted in an automatic voltage regulator system. In: 2022 Global Energy Conference (GEC). Batman: IEEE, 2022, 262–265

[41]

Izci D , Ekinci S , Eker E , Kayri M . Augmented hunger games search algorithm using logarithmic spiral opposition-based learning for function optimization and controller design. Journal of King Saud University-Engineering Sciences, 2024, 36(5): 330–338

[42]

Liu K, Chen F X, Zeng L Z. Fluctuation analysis of electromagnetic force in magnetic levitation planar motor. In: 2024 International Conference on Control, Automation and Robotics (ICCAR). Singapore: IEEE, 2024, 283–288

[43]

Oustaloup A , Levron F , Mathieu B , Nanot F M . Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2000, 47(1): 25–39

Rights & permissions

Higher Education Press

PDF (4835KB)

20

Accesses

0

Citation

Detail

Sections
Recommended

/